Exact Solution of Bipartite Fluctuations in One-Dimensional Fermions

• URL: http://arxiv.org/abs/2403.18523v3
• Date: Thu, 26 Dec 2024 11:11:51 GMT
• Title: Exact Solution of Bipartite Fluctuations in One-Dimensional Fermions
• Authors: Kazuya Fujimoto, Tomohiro Sasamoto,
• Abstract summary: Emergence of hydrodynamics in quantum many-body systems has recently garnered growing interest. We theoretically study the variance of a bipartite fluctuation in one-dimensional noninteracting fermionic dynamics. Our exact solutions and numerical findings here lay a foundation for growing bipartite fluctuations in quantum many-body dynamics.
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• Abstract: Emergence of hydrodynamics in quantum many-body systems has recently garnered growing interest. The recent experiment of ultracold atoms [J. F. Wienand {\it et al.}, Nat. Phys. (2024), doi:10.1038/s41567-024-02611-z] studied emergent hydrodynamics in hard-core bosons using a bipartite fluctuation, which quantifies how the particle number fluctuates in a subsystem. In this Letter, we theoretically study the variance of a bipartite fluctuation in one-dimensional noninteracting fermionic dynamics starting from an alternating state, deriving the exact solution of the variance and its asymptotic linear growth law for the long-time dynamics. To compare the theoretical prediction with the experiment, we generalize our exact solution by incorporating the incompleteness of the initial alternating state, deriving the general linear growth law analytically. We find that it shows good agreement with the experimentally observed variance growth without any fitting parameters. Furthermore, we estimate a time scale for the local equilibration using our exact solution, finding that the time scale is independent of the initial incompleteness. To investigate the interaction effect, we implement numerical studies for the variance growth in interacting fermions, which has yet to be explored experimentally. As a result, we find that the presence of interactions breaks the linear variance growth derived in the noninteracting fermions. Our exact solutions and numerical findings here lay a foundation for growing bipartite fluctuations in quantum many-body dynamics.

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